Is there any software to do so, and what would it take to install it?
Another person had physical access to my phone, so I suspect the possibility of installation of such software.
Even photos which I immediately deleted and those, which went straight to application got in other hands.
I have an iPhone 4s. It was not jailbroken (at least, by me), and it did not appear such: no Cydia app or other oddities.
Photo Stream and iCloud backup for photos were also off, and I never used them.